cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 13 results. Next

A241249 Number of nX2 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

3, 5, 17, 39, 87, 212, 488, 1134, 2644, 6118, 14205, 32964, 76395, 177149, 410798, 952422, 2208198, 5120116, 11871494, 27525169, 63821315, 147978217, 343107782, 795547902, 1844596244, 4276972393, 9916824861, 22993686321, 53314396437
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Column 2 of A241255

Examples

			Some solutions for n=4
..3..3....3..3....2..2....2..2....2..2....3..3....3..2....2..2....3..3....2..2
..2..1....2..2....3..1....3..1....3..1....2..1....0..3....3..1....2..2....3..1
..3..1....0..2....0..2....3..1....3..2....0..2....0..2....3..1....3..2....2..1
..3..3....3..2....3..3....3..2....3..2....0..3....0..2....2..1....3..1....2..2
		

Formula

Empirical: a(n) = 3*a(n-2) +14*a(n-3) +5*a(n-4) -28*a(n-5) -89*a(n-6) -50*a(n-7) +93*a(n-8) +303*a(n-9) +214*a(n-10) -113*a(n-11) -561*a(n-12) -468*a(n-13) -47*a(n-14) +584*a(n-15) +499*a(n-16) +142*a(n-17) -359*a(n-18) -96*a(n-19) -23*a(n-20) +128*a(n-21) -102*a(n-22) -99*a(n-23) -119*a(n-24) +32*a(n-25) +82*a(n-26) +113*a(n-27) +50*a(n-28) -7*a(n-29) -42*a(n-30) -20*a(n-31) +a(n-32) +4*a(n-33) +a(n-34) for n>37

A241250 Number of nX3 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 4, 13, 47, 174, 606, 2111, 6647, 21752, 70595, 229009, 744946, 2418238, 7843143, 25449403, 82556576, 267788667, 868709237, 2817909735, 9140802924, 29651305001, 96183371668, 311999852696, 1012067748968, 3282944840574, 10649213948821
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Column 3 of A241255

Examples

			Some solutions for n=4
..3..3..2....2..2..3....3..3..2....3..3..2....2..2..3....3..3..2....3..3..2
..2..1..3....3..1..2....2..1..3....2..1..3....3..1..2....2..1..3....2..1..1
..2..2..3....2..1..3....2..2..3....2..1..3....2..1..3....2..1..3....2..2..2
..0..0..2....2..2..2....2..1..3....2..0..1....2..2..3....2..0..2....2..1..2
		

A241251 Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

7, 10, 34, 120, 545, 2570, 13328, 70264, 390840, 2166393, 12186519, 68347761, 385756287, 2171706653, 12264859070, 69159861508, 390555507284, 2203677274384, 12443050758381, 70227871631917, 396507191404589, 2238145931844904
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Column 4 of A241255

Examples

			Some solutions for n=4
..3..3..2..2....3..3..2..2....3..3..2..2....3..3..2..3....2..2..3..3
..2..1..3..1....2..1..3..1....2..1..3..1....2..1..1..2....0..0..2..1
..2..2..2..1....2..2..3..1....0..2..0..1....2..2..0..2....0..0..0..2
..2..1..2..1....2..1..3..2....0..3..2..3....0..0..0..2....3..3..0..1
		

A241256 Number of 2 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 5, 4, 10, 12, 22, 41, 59, 120, 171, 306, 494, 784, 1345, 2112, 3547, 5782, 9402, 15643, 25307, 41868, 68465, 112078, 184535, 301346, 495580, 811726, 1330658, 2184497, 3577622, 5872217, 9625155, 15783147, 25889388, 42437724, 69611469, 114132047
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Examples

			Some solutions for n=4:
..3..3..2..2....2..2..3..3....2..2..3..3....2..2..3..3....2..2..3..3
..2..1..3..1....3..1..2..1....0..0..0..2....3..1..0..2....0..0..2..1
		

Crossrefs

Row 2 of A241255.

Formula

Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) - a(n-5) - a(n-6) + a(n-7) + 2*a(n-8) + a(n-10) for n>12.
Empirical g.f.: x*(2 + 5*x - 4*x^3 - 4*x^4 + x^5 + 8*x^6 + 8*x^7 + 11*x^8 + x^9 + 3*x^10 - 3*x^11) / ((1 + x)*(1 - x - x^2 - x^3 + 2*x^4 - x^5 + 2*x^6 - 3*x^7 + x^8 - x^9)). - Colin Barker, Oct 29 2018

A241257 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 17, 13, 34, 71, 135, 356, 734, 1705, 3914, 8291, 19714, 42700, 93528, 214479, 462299, 1030477, 2304077, 5035291, 11240675, 24870524, 54876698, 121998539, 269425049, 596725510, 1322494224, 2923575132, 6478965125, 14341026682
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Row 3 of A241255

Examples

			Some solutions for n=4
..2..2..3..2....3..3..2..2....2..2..3..3....2..2..3..2....3..3..2..2
..0..0..0..3....2..1..3..1....0..0..2..1....0..0..0..3....2..1..3..1
..0..3..1..2....0..2..0..2....0..0..0..3....0..0..2..2....0..2..2..2
		

Formula

Empirical: a(n) = 5*a(n-2) +12*a(n-3) -10*a(n-4) -49*a(n-5) -32*a(n-6) +99*a(n-7) +157*a(n-8) -89*a(n-9) -342*a(n-10) -104*a(n-11) +431*a(n-12) +412*a(n-13) -199*a(n-14) -494*a(n-15) -154*a(n-16) -16*a(n-17) +1491*a(n-18) +1405*a(n-19) -1976*a(n-20) -3729*a(n-21) -239*a(n-22) +1932*a(n-23) +2761*a(n-24) -1387*a(n-25) +1240*a(n-26) +884*a(n-27) -1768*a(n-28) -1322*a(n-29) +738*a(n-30) -734*a(n-31) -1142*a(n-32) -314*a(n-33) +2396*a(n-34) +196*a(n-35) -1802*a(n-36) +778*a(n-37) +1882*a(n-38) -1840*a(n-39) -1356*a(n-40) +744*a(n-41) -900*a(n-42) -560*a(n-43) +220*a(n-44) -104*a(n-45) -32*a(n-46) +244*a(n-47) +24*a(n-48) -72*a(n-49) +56*a(n-50) -24*a(n-52) for n>59

A241258 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

6, 39, 47, 120, 446, 1202, 3822, 11428, 35540, 119334, 350064, 1176852, 3642784, 10937680, 36354323, 110544260, 342643258, 1103393347, 3372356997, 10609585314, 33372515121, 103547161107, 325451014192, 1015953932945, 3176715059861
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Row 4 of A241255

Examples

			Some solutions for n=4
..2..2..3..3....2..2..3..2....2..2..3..3....2..2..3..3....3..3..2..2
..3..1..2..2....3..1..0..3....0..0..2..1....3..1..2..1....2..1..3..1
..2..2..3..3....2..1..1..2....0..0..2..2....2..2..2..2....0..2..0..1
..0..2..1..2....2..2..3..2....0..0..0..3....2..0..0..1....0..0..2..2
		

A241259 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

8, 87, 174, 545, 3404, 11700, 50281, 252069, 959723, 5014754, 21265779, 97686188, 454095979, 1911405908, 9090872300, 40760423923, 177043945473, 836152068055, 3685193095173, 16440527244397, 75962562059779, 337317605161865
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Row 5 of A241255

Examples

			Some solutions for n=3
..2..2..3....2..2..3....2..2..3....3..3..2....3..3..2....3..3..2....2..2..3
..3..1..2....0..0..2....0..0..2....2..1..3....2..1..3....2..1..3....3..1..2
..2..1..3....0..0..2....0..0..2....2..2..2....0..2..2....2..2..3....2..1..2
..2..2..3....0..0..2....0..0..2....2..1..2....0..3..2....0..0..3....2..1..2
..2..1..2....0..0..3....0..3..3....2..1..2....2..0..2....0..0..2....2..0..2
		

A241248 Number of n X n 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 5, 13, 120, 3404, 124372, 13138271, 8317272277
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Diagonal of A241255

Examples

			Some solutions for n=4
..3..3..2..2....2..2..3..3....2..2..3..3....2..2..3..3....3..3..2..2
..2..1..3..1....3..1..0..2....0..0..2..1....3..1..0..2....2..1..3..1
..2..2..2..2....3..2..1..2....0..3..2..3....3..2..1..2....2..2..0..2
..2..0..0..2....3..2..1..2....3..2..1..2....2..2..3..2....0..0..3..2
		

A241252 Number of n X 5 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

10, 12, 71, 446, 3404, 25190, 225191, 2057343, 20539926, 204332167, 2101549932, 21494785659, 224464995283, 2317825938537, 24259559536660, 251621814311194, 2633451197372065, 27369019127795259
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Column 5 of A241255.

Examples

			Some solutions for n=4:
..3..3..2..2..2....2..2..2..2..3....3..3..2..2..2....2..2..2..2..3
..2..1..3..1..1....0..0..0..0..2....2..1..3..0..1....0..0..0..0..2
..0..2..2..2..2....3..3..0..0..2....2..2..0..0..2....0..0..0..0..2
..0..0..0..0..2....0..2..1..1..2....2..1..2..3..2....0..0..3..1..2
		

Crossrefs

Cf. A241255.

A241253 Number of nX6 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

15, 22, 135, 1202, 11700, 124372, 1558957, 22016913, 362503120, 6317232175, 119650082800
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Column 6 of A241255

Examples

			Some solutions for n=4
..3..3..2..3..3..2....3..3..2..2..2..3....3..3..2..2..2..3....3..3..2..2..2..3
..2..1..1..2..1..1....2..1..1..0..0..2....2..1..3..0..1..1....2..1..3..0..1..1
..2..2..2..2..2..2....0..2..0..0..0..2....0..2..0..1..2..1....0..2..0..1..2..1
..0..0..2..0..0..2....2..0..2..0..0..2....0..0..0..2..2..2....2..0..0..2..2..2
		
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